*Esta oración tiene sentido? *Puedo decir
(Yo) lo habría abierto con mis dientes.
'Lo' is for things of unspecified gender. If you had already mentioned a feminine object like say, a bottle (una botella) then you could say 'la habría abierto con mis dientes.'
We are using the conditional perfect tense here, which is haber in the conjugated state plus participle. Habría abrirlo isn't correct because you have the conjugated form of 'haber' but then an infinitive (abrir). The grammar is actually the same as in English (would have = habría, abierto = opened.)